Method for calculating survival coefficients

ABSTRACT

WHEREIN X11=D1 AND WHEREIN FOR I&gt;1   SUCH THAT (4) O$XIJ$GI-1, J-1-GI-1, J WHEREIN J=I, ..., I AND   (5) XIJ=O WHEREVER J&gt;I OR J&gt;C     A METHOD OF DETERMINING THE VALUES OF THE TERM HF IN THE RELIABLITY EQUATION FOR A STORAGE ORGANIZATION:   WHEREIN PF IS THE PROBABILITY OF THERE BEING F FAILURES IN THE ORGANIZATION AND WHEREIN THE VALUES OF HF ARE THE SURVIVAL COEFFICIENTS, THE STORAGE ORGANIZATION COMPRISING A QUANTITY OF 1 WORDS OF N-BIT LENGTH, AND BEING CON-   STRUCT SO AS TO CORRECT A QUANTITY OF C ERRORS. THE METHOD COMPRISES: (A) GENERATING SURVIVAL PATTERNS FOR GIVEN VALUES OF C, F, N AND I WHEREIN THERE ARE CONSIDERED ALL OF THE AR RAYS   S11 S12 . . . S11 SS21 22 . . . .S21 . . . .   SN1 SN2 . . . SN1   WHEREIN SIJ IS THE NUMBER OF FAILURES IN THE ITH BIT OF THE ITH WORD WITH   SUCH THAT   D R A W I N G AND WHEREIN THE TERM AM IS DEFINED AS THE NUMBER OF R1=M FOR M=O,..., F, THE TERM BIM IS DEFINED AS BEING EQUAL TO THE NUMBER OF SIK=M FOR M =1, ..., F, THE TERM DI IS DEFINED AS   AND WHEREIN   THE PRIMITIVES BEING MODIFIED BY SHIFTING EACH ROW THEREOF SUFFICIENTLY TO THE RIGHT TO FIT A GIVEN SET OF REPLICATION NUMBERS (XIJ) WHEREIN XIJ IS EQUAL TO THE NUMBER OF NONZERO POSITIONS INTRODUCED FOR THE JTH TIME IN THE ITH ROW WHEREBY, FOR ANY GIVEN PRIMITIVE, THE RANGE OF REPLICATION NUMBERS, ALL OF WHICH PRODUCE SURVIVAL PATTERNS, ARE DETERMINED AS FOLLOWS: AND MULTIPLYING THAT PROBABILITY BY THE NUMBER OF PERMUTATIONS, AND (D) SUMMING ALL OF THE PRODUCTS RESULTING FROM STEP (C) OVER ALL OF THE GENERIC SURVIVAL PATTERN.   (C) CALCULATING THE PROBABILITY OF THE OCCURRENCE OF EACH PATTERN IN ACCORDANCE WITH THE FOLLOWING EXPRESSION   (B) CALCULATING THE NUMBER OF PERMUTATIONS OF EACH SURVIVAL PATTERN IN ACCORDANCE WITH THE EQUATION:

PUBLICATION UNITED STATES PATENT OFFICE Published at the request of the applicant or owner in accordance with the Notice of Dec. 16, 1969, 869 0.6. 687. The abstracts of Defensive Publication applications are identified by distinctly numbered series and are arranged chronologically. The heading of each abstract indicates the number of pages of specification, including claims and sheets of drawings contained in the application as originally filed. The files or these applications are available to the public for inspection and reproduction may be purchased for 30 cents a sheet.

Defensive Publication applications have not been examined as to the merits 0t alleged invention. The Patent Oflice makes no assertion as to the novelty of the disclosed subject matter.

PUBLISHED JULY 10, 1973 T912,004 METHOD FOR CALCULATING SURVIVAL COEFFICIENTS Willard G. Bouricius, Katonah, and Betty J. Schultz, New Rochelle, N.Y., assignors to International Business Machines Corporation, Armonk, N.Y.

Filed June 30, 1972, Ser. No. 267,826 Int. Cl. G06f 7/00, 9/00; G06h 15/34,

US. Cl. 444--1 2 Sheets Drawing. 32 Pages Specification INITIALIZE AN ARRAY TO REPRESENT THE URN MODEL OF THE REAL PHYSICAL ENTITY I2 I OENERATE THE FIRST GENERIC PATTERN INITIALIZE AN AOOUHULATOR TO THE PRODUCT OF in) THE PROBABILITY OF THIS FIRST PATTERN'S 'OOOURRING AND (b) THE NUMBER OF PERMUTATIONS FOR THIS FIRST PATTERN 16 GENERATE THE NEXT GENERIC PATTERN IB' 1 COIIPUTE THE PROBABILITY OF THIS PATTERNS OOOURRING I 2 1 COMPUTE THENUMBEROF PERMUTATIOHS or nus PATTERN I 22 1 MULTIPLY THE PROBABILITY BY THE NUMBER OF PERIIUTATIONS J 24 1 ADD nus PRODUCT TO THE ACCUHULATOR J 26] TEST FOR HAVING EXHAUSTEO ALL OF THE PATTERN A method of determining the values of the term H in the reliability equation for a storage organization:

ater-e 2 f wherein P; is the probability of there being 1 failures in the organization and wherein the values of H; are the survival coefiicients, the storage organization comprising a quantity of 1 Words of 11-bit length, and being constructed so as to correct a quantity of 0 errors. The method comprises:

(a) Generating survival patterns for given values of c, f, n and I wherein there are consideredall of the arrays S8 S S nl n2 nl wherein S is the number of failures in the ith bit of the jth Word with l RFZSII such that a 2 i f R12R1+1 for i=1, o (3) S 2S for k=l, (l1) and wherein the term A is defined as the number of R =m for m=0, f, the term B is defined as being equal to the number of S =m for m'=l, f, the term D is defined as and wherein f 2 H m=0 the primitives being modified by shifting each row thereof sufficiently to the right to lit a given set of replication numbers (X wherein X is equal to the number of nonzero positions introduced for the jth time in the ith row whereby, for any given primitive, the range of replication numbers, all of which produce survival patterns, are determined as follows:

PUBLISHED JULY 10, 1973 (b) Calculating the number of permutations of each survival pattern in accordance with the equation:

(c) Calculating the probability of the occurrence of each pattern in accordance with the following expression f! U H ik) lc=1, ,l and multiplying that probability by the number of permutations; and

(d) Summing all of the products resulting from step (c) over all of the generic survival patterns.

July 10,

Filed June 30, 1972 1973 w c us ET AL 1912,00 4

METHOD FOR CALCULATING SURVIVAL COEFFICIENTS 2 Sheets-Sheet ll. FIG.I

INITIALIZE AN ARRAY TO REPRESENT THE URN MODEL OFTHE REAL PHYSICAL ENTITY GENERATE THE FIRST GENERIC PATTERN INITIALIZE AN ACCUMULATOR TO THE PRODUCT OF (0) THE PROBABILITY OF THIS FIRST PATTERN'S OCCURRING AND (b) THE NUMBER OF PERMUTATIONS FOR THIS FIRST PATTERN CENERATE THE NEXT GENERIC PATTERN COMPUTE THE PROBABILITY OF THIS PATTERN 'S OCCURRINC COMPUTE THE NUMBER OF PERMUTATIONS OF THIS PATTERN MULTIPLY THE PROBABILITY BY THE NUMBER OF PERMUTATIONS ADD THIS PRODUCT TO THE ACCUMULATOR TEST FOR HAVING EXHAUSTED ALL OF THE PATTERN YES NO 28 STOP My 10? 1973 w. G- BOURICIUS ET AL T912,004

METHOD FOR CALCULATING SURVIVAL COEFFICIENTS Filed June so, 1972 2 sheets-sheet STORE=N L Q ARRAY=F F FIG. 2 ARRA= IIXKK F *ARRA ARRAY STORE 

